You can almost always evict someone simply for not paying rent, you don't need anything else usually. In MO the only way to get someone out faster is if it is an unsafe situation for someone else, usually a roommate evicting another roommate.
Letting the legal system work is usually the only way to deal with it, but you can sometimes try to offer the resident something to give back possession for some sort of compensation (dropped eviction charges, deposit refund, cash, moving truck etc...) This can often be the correct business decision even if it favors someone who already hurt you financially.
Different states have different laws making the process always take a different amount of time. In states where it takes awhile to evict it is extremely important to screen well and get a quality person who cares about their background into the property. That way they will likely keep the property up and pay, but if they don't they will be reasonable with a plan to move them out to prevent negative history on their background while you can get possession of the property back quickly to re-rent it.